Geodesic
On the p-domination number of cactus graphs
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 355-361.

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Let p be a positive integer and G = (V,E) a graph. A subset S of V is a p-dominating set if every vertex of V-S is dominated at least p times. The minimum cardinality of a p-dominating set a of G is the p-domination number γₚ(G). It is proved for a cactus graph G that γₚ(G) ⩽ (|V| + |Lₚ(G)| + c(G))/2, for every positive integer p ⩾ 2, where Lₚ(G) is the set of vertices of G of degree at most p-1 and c(G) is the number of odd cycles in G.
Keywords: p-domination number, cactus graphs 
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Blidia, Mostafa; Chellali, Mustapha; Volkmann, Lutz. On the p-domination number of cactus graphs. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 355-361. http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a12/

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